Contents
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What is TemperatureThe Development of
Thermometers and Temperature ScalesHeat and ThermodynamicsThe Kinetic TheoryThermal Radiation3 K - The Temperature of the Universe
SummaryAcknowledgmentsReferences

The earliest devices used to measure the temperature were called thermoscopes.

They consisted of a glass bulb having
a long tube extending downward into a container of colored water, although Galileo
in 1610 is supposed to have used wine. Some of the air in the bulb was expelled
before placing it in the liquid, causing the liquid to rise into the tube. As
the remaining air in the bulb was heated or cooled, the level of the liquid
in the tube would vary reflecting the change in the air temperature. An engraved
scale on the tube allowed for a quantitative measure of the fluctuations.

The air in the bulb is referred to as the thermometric medium, i.e.
the medium whose property changes with temperature.

In 1641, the first sealed thermometer that used liquid rather than air as
the thermometric medium was developed for Ferdinand II, Grand Duke of Tuscany.
His thermometer used a sealed alcohol-in-glass device, with 50 "degree" marks
on its stem but no "fixed point" was used to zero the scale. These were referred
to as "spirit" thermometers.

Robert Hook, Curator of the Royal Society, in 1664 used a red dye in the alcohol
. His scale, for which every degree represented an equal increment of volume
equivalent to about 1/500 part of the volume of the thermometer liquid, needed
only one fixed point. He selected the freezing point of water. By scaling it
in this way, Hook showed that a standard scale could be established for thermometers
of a variety of sizes. Hook's original thermometer became known as the standard
of Gresham College and was used by the Royal Society until 1709. (The first
intelligible meteorological records used this scale).

In 1702, the astronomer Ole Roemer of Copenhagen based his scale upon two
fixed points: snow (or crushed ice) and the boiling point of water,
and he recorded the daily temperatures at Copenhagen in 1708- 1709 with this
thermometer.

It was in 1724 that Gabriel Fahrenheit, an instrument maker of Däanzig
and Amsterdam, used mercury as the thermometric liquid. Mercury's thermal expansion
is large and fairly uniform, it does not adhere to the glass, and it remains
a liquid over a wide range of temperatures. Its silvery appearance makes it
easy to read.

Fahrenheit described how he calibrated the scale of his mercury thermometer:

"placing the thermometer in a mixture of sal ammoniac or sea salt,
ice, and water a point on the scale will be found which is denoted as zero.
A second point is obtained if the same mixture is used without salt. Denote
this position as 30. A third point, designated as 96, is obtained if the thermometer
is placed in the mouth so as to acquire the heat of a healthy man." (D. G. Fahrenheit,Phil.
Trans. (London) 33, 78, 1724)

On this scale, Fahrenheit measured the boiling point of water to be 212. Later
he adjusted the freezing point of water to 32 so that the interval between the
boiling and freezing points of water could be represented by the more rational
number 180. Temperatures measured on this scale are designated as degrees
Fahrenheit (° F).

In 1745, Carolus Linnaeus of Upsula, Sweden, described a scale in which the
freezing point of water was zero, and the boiling point 100, making it a centigrade
(one hundred steps) scale. Anders Celsius (1701-1744) used the reverse scale
in which 100 represented the freezing point and zero the boiling point of water,
still, of course, with 100 degrees between the two defining points.

In 1948 use of the Centigrade scale was dropped in favor of a new scale using
degrees Celsius (° C). The Celsius scale is defined by
the following two items that will be discussed later in this essay:

(i) The triple point of water is defined to be 0.01° C.
(ii) A degree Celsius equals the same temperature change as a degree on the
ideal-gas scale.

On the Celsius scale the boiling point of water at standard atmospheric pressure
is 99.975 C in contrast to the 100 degrees defined by the Centigrade scale.

In 1780, J. A. C. Charles, a French physician, showed that for the same
increase in temperature, all gases exhibited the same increase in volume.
Because the expansion coefficient of gases is so very nearly the same, it
is possible to establish a temperature scale based on a single fixed point
rather than the two fixed- point scales, such as the Fahrenheit and Celsius
scales. This brings
us back to a thermometer that uses a gas as the thermometric medium.

In a constant volume gas thermometer a
large bulb B of gas, hydrogen for example, under a set pressure connects with
a mercury-filled "manometer" by means of a tube of very small volume.
(The Bulb B is the temperature-sensing portion and should contain almost all
of the hydrogen). The level of mercury at C may be adjusted by raising or
lowering the mercury reservoir R. The pressure of the hydrogen gas, which is
the "x" variable in the linear relation with temperature, is the difference
between the levels D and C plus the pressure above D.

P. Chappuis in 1887 conducted extensive studies of gas thermometers with
constant pressure or with constant volume using hydrogen, nitrogen, and
carbon dioxide as the thermometric medium. Based on his results, the
Comité International des Poids et Mesures adopted the
constant-volume
hydrogen scale based on fixed points at the ice point (0° C) and the
steam point (100° C) as the practical scale for international meteorology.

Experiments with gas thermometers have shown that there is very little
difference in the temperature scale for different gases. Thus, it is
possible to set up a temperature scale that is independent of the
thermometric medium if it is a gas at low pressure. In this case, all
gases behave like an "Ideal Gas" and have a very simple relation between
their pressure, volume, and temperature:

pV= (constant)T.

This temperature is called the thermodynamic temperature and is
now accepted as the fundamental measure of temperature. Note that there is a
naturally-defined zero on this scale - it is the point at which
the pressure of
an ideal gas is zero, making the temperature also zero. We will continue
a discussion of "absolute zero" in a later section. With this as one point on
the scale, only one other fixed point need be defined. In 1933, the
International Committee of Weights and Measures adopted this fixed point as
the triple point of water , the temperature at which
water, ice, and water vapor coexist in equilibrium); its value is set as
273.16. The unit of temperature on this scale is called the kelvin, after
Lord Kelvin (William Thompson), 1824-1907, and its
symbol is K (no degree symbol used).

To convert from Celsius to Kelvin, add 273.

K = ° C + 273.

Thermodynamic temperature is the fundamental temperature;
its unit is the kelvin which is defined as the fraction 1/273.16 of the
thermodynamic temperature of the triple point of water.

Sir William Siemens, in 1871, proposed a thermometer whose thermometric
medium is a metallic conductor whose resistance changes with temperature.
The element platinum does not oxidize at high temperatures and has a
relatively uniform change in resistance with temperature over a large
range. The Platinum Resistance Thermometer is now widely used as a
thermoelectric thermometer and covers the temperature range from
about -260° C to 1235° C.

Several temperatures were adopted as Primary reference
points so as to define the International Practical Temperature Scale of
1968. The International Temperature Scale of 1990 was adopted by the
International Committee of Weights and Measures at its meeting in 1989.
Between 0.65K and 5.0K, the temperature is defined in terms of the vapor
pressure - temperature relations of the isotopes of helium. Between 3.0K
and
the triple point of neon (24.5561K) the temperature is defined by means of
a helium gas thermometer. Between the triple point of hydrogen (13.8033K)
and the freezing point of silver (961.78°K) the
temperature is defined
by means of platinum resistance thermometers. Above the freezing point of
silver the temperature is defined in terms of the Planck radiation law.

T. J. Seebeck, in 1826, discovered that when wires of different metals are
fused at one end and heated, a current flows from one to the other. The electromotive
force generated can be quantitatively related to the temperature and hence,
the system can be used as a thermometer - known as a thermocouple. The thermocouple
is used in industry and many different metals are used - platinum and platinum/rhodium,
nickel-chromium and nickel-aluminum, for example. The National Institute of
Standards and Technology (NIST)
maintains databases for standardizing thermometers.

For the measurement of very low temperatures, the magnetic susceptibility
of a paramagnetic substance is used as the thermometric physical quantity. For
some substances, the magnetic susceptibility varies inversely as the temperature.
Crystals such as cerrous magnesium nitrate and chromic potassium alum have been
used to measure temperatures down to 0.05 K; these crystals are calibrated in
the liquid helium range. This diagram and the last
illustration in this text were taken from the Low Temperature Laboratory, Helsinki
University of Technology's picture archive. For these
very low, and even lower, temperatures, the thermometer is also the mechanism
for cooling. Several low-temperature laboratories conduct
interesting applied and theoretical research on how to reach the lowest possible
temperatures and how work at these temperatures may find application.

A second statement may also be made about how machines operate. A steam
engine uses a source of heat to produce work. Is it possible to
completely convert the heat energy into work, making it a 100% efficient
machine? The answer is to be found in the second law of
thermodynamics:

No cyclic machine can convert heat energy wholly into other forms of energy.
It is not possible to construct a cyclic machine that does nothing but
withdraw heat energy and convert it into mechanical energy.

The second law of thermodynamics implies the irreversibility of certain
processes - that of converting all heat into mechanical energy, although it
is possible to have a cyclic machine that does nothing but convert mechanical
energy into heat!

Sadi Carnot (1796-1832) conducted theoretical studies
of the efficiencies
of heat engines (a machine which converts
some of its heat into useful work). He was trying to model the most
efficient
heat engine possible. His theoretical work provided the basis for practical
improvements in the steam engine and also laid the foundations of
thermodynamics. He described an ideal engine, called the Carnot engine,
that is the most efficient way an engine can be constructed. He showed
that the efficiency of such an engine is given by

efficiency = 1 - T"/T',

where the temperatures, T' and T" , are the hot and cold "reservoirs" ,
respectively, between which the machine operates. On this temperature scale,
a heat engine whose coldest reservoir is zero degrees would operate with 100%
efficiency. This is one definition of absolute zero, and it can be
shown to be identical to the absolute zero we discussed previously.
The temperature scale is called the absolute, the thermodynamic
, or the kelvin scale.

The way that the gas temperature scale and the thermodynamic temperature
scale are shown to be identical is based on the microscopic
interpretation of temperature, which postulates that the
macroscopic measurable quantity called temperature is a result
of the random motions of the microscopic particles that make up a system.

About the same time that thermodynamics was evolving,
James Clerk Maxwell
(1831-1879) and Ludwig Boltzmann (1844-1906)
developed a theory describing
the way molecules moved - molecular dynamics. The molecules that make up a
perfect gas move about, colliding with each other like billiard balls and
bouncing off the surface of the container holding the gas. The energy
associated with motion is called Kinetic Energy and this kinetic approach to
the behavior of ideal gases led to an interpretation of the concept of
temperature on a microscopic scale.

The amount of kinetic energy each molecule has is a function of its velocity;
for the large number of molecules in a gas (even at low pressure), there
should be a range of velocities at any instant of time. The magnitude of
the velocities of the various particles should vary greatly - no two
particles should be expected to have the exact same velocity. Some may be
moving very fast; others, quite slowly. Maxwell found that he could
represent the distribution of velocities statistically by a function known
as the Maxwellian distribution. The collisions of
the molecules with their container gives rise to the pressure of the gas.
By considering the average force exerted by the molecular collisions on the
wall, Boltzmann was able to show that the average kinetic energy of the
molecules was directly comparable to the measured pressure, and the greater
the average kinetic energy, the greater the pressure. From Boyles' Law, we
know
that the pressure is directly proportional to the temperature, therefore,
it was shown that the kinetic energy of the molecules related directly to
the temperature of the gas. A simple relation holds for this:

average kinetic energy of molecules=3kT/2,

where k is the Boltzmann
constant. Temperature is a measure of the
energy of thermal motion and, at a temperature of zero, the energy reaches
a minimum (quantum mechanically, the zero-point motion remains at
0 K).

Dealing with a system which contained huge numbers of molecules requires a
statistical approach to the problem. About 1902, J. W. Gibbs (1839-1903) introduced statistical
mechanics with which he
demonstrated how average values of the properties of a system could be
predicted from an analysis of the most probable values of these properties
found from a large number of identical systems (called an ensemble). Again,
in the statistical mechanical interpretation of thermodynamics, the key
parameter is identified with a temperature which can be directly linked to
the
thermodynamic temperature, with the temperature of Maxwell's distribution,
and with the perfect gas law.

Temperature becomes a quantity definable either in terms of
macroscopic thermodynamic quantities such as heat and work, or, with equal
validity and identical results, in terms of a quantity which characterized
the energy distribution among the particles in a system. (Quinn,
"Temperature")

With this understanding of the concept of temperature, it is possible to
explain how heat (thermal energy) flows from one body to another.
Thermal energy is carried by the molecules in the form of their motions and
some of it, through molecular collisions, is transferred to molecules of a
second object when put in contact with it. This mechanism for transferring
thermal energy by contact is called conduction.

A second mechanism of heat transport is illustrated by a pot of water set
to boil on a stove - hotter water closest to the flame will rise to mix with
cooler water near the top of the pot. Convection involves the bodily
movement of the more energetic molecules in a liquid or gas.

The third way that heat energy can be transferred from one body to another
is by radiation; this is the way that the sun warms the earth. The
radiation
flows from the sun to the earth, where some of it is absorbed, heating the
surface.

A major dilemma in physics since the time of Newton was how to explain
the nature of this radiation.

The curves illustrated below show that the hotter the body is,
the brighter it is at shorter wavelengths. The surface
temperature of the
sun is 6000 K, and its Planck curve peaks in the visible wavelength range.
For bodies cooler than the sun, the peak of the Planck curve shifts to longer
wavelengths, until a temperature is reached such that very little radiant
energy is emitted in the visible range.

This figure (adapted from Adkins' "Thermal Physics") shows several
Planck curves for black bodies. The Intensity is in units of energy per
unit area per unit solid angle per unit time per unit wavelength interval.
The broken line illustrates
the
variation with wavelength and temperature of the peaks of the curves.

This is a graphical representation of Wien's law, which states:

(max) ~ 0.29/T,

where (max) is the wavelength of maximum brightness
in cm and T is the absolute temperature of the black body.

The sun and stars emit thermal
radiation covering all wavelengths; other objects in the sky, like the
great clouds of gas in the Milky Way, also emit thermal radiation but are
much cooler. These objects are best detected by infrared and radio telescopes
- telescopes whose detectors are sensitive to the longer wavelengths.

In 1965, Arno Penzias and Robert Wilson were conducting a careful
calibration of their radio telescope at the Bell Laboratory at Whippany,
New Jersey. The found that their receiver showed a "noise" pattern as if it
were inside a container whose temperature was 3K - i.e. as if it were in
equilibrium with a black body at 3 K. This "noise" seemed to be
coming from every direction. Earlier theoretical predictions by George
Gamow and other astrophysicists had predicted the existence of a
cosmic 3
K background. Penzias' and Wilson's discovery was the observational
confirmation of the
isotropic radiation from the Universe, believed to be a relic of the "Big
Bang".
The enormous thermal energy released during the creation of the universe
began to cool as the universe expanded. Some 12 billion years later, we are
in a universe that radiates like a black body now cooled to 3 K. In
1978 Penzias and Wilson were awarded the Nobel prize in physics for this
discovery.

A black body at 3 K emits most of its energy in the microwave wavelength range.
Molecules in the earth's atmosphere absorb this radiation so that from the ground,
astronomers cannot make observations in this wavelength region. In 1989 the
Cosmic Background Explorer (COBE) satellite, developed
by NASA's Goddard Space Flight Center, was
launched to measure the diffuse infrared and microwave radiation from the early
universe. One of its instruments, the Far Infrared Absolute Spectrophotometer
(FIRAS) compared the spectrum of the cosmic microwave background radiation with
a precise blackbody. The cosmic microwave background spectrum
was measured with a precision of 0.03% and it fit precisely with a black body
of temperature 2.726 K. Even though there are billions of stars in the universe,
these precise COBE measurements show that 99.97% of the radiant energy of the
Universe was released within the first year after the Big Bang itself and now
resides in this thermal 3 K radiation field.

A more detailed
explanation of the origin of the microwave background radiation, and its
possible anisotropy,
may be found here. A new mission
selected by NASA is the Microwave
Anisotropy Probe (MAP) will measure the
small fluctuations in the background radiation and will yield more
information on the details of the early universe. The European Space
Agency has a similar mission
planned.

One of the beauties of "publishing" on the web is the interactive element
it offers. Joachim Reinhardt has written to point out
that the highest temperatures that are accessible on earth (only surpassed
by the early stages of the big bang) occur in high-energy collisions of
particles (in particular of heavy ions), during which one sees a "fireball"
with a temperature of several hundred MeV (which corresponds
to a temperature of 10 to the 12th power k). This fireball cools down by
expanding
and by radiating off particles, mostly pions, quite similar to the thermal
black-body radiation.

Thermal physics is a field rich in theoretical and practical applications.